// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_HYPERPLANE_H
#define EIGEN_HYPERPLANE_H

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
 *
 * \class Hyperplane
 *
 * \brief A hyperplane
 *
 * A hyperplane is an affine subspace of dimension n-1 in a space of dimension n.
 * For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.
 *
 * \tparam _Scalar the scalar type, i.e., the type of the coefficients
 * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
 *             Notice that the dimension of the hyperplane is _AmbientDim-1.
 *
 * This class represents an hyperplane as the zero set of the implicit equation
 * \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is a unit normal vector of the plane (linear part)
 * and \f$ d \f$ is the distance (offset) to the origin.
 */
template<typename _Scalar, int _AmbientDim, int _Options>
class Hyperplane
{
  public:
	EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,
															   _AmbientDim == Dynamic ? Dynamic : _AmbientDim + 1)
	enum
	{
		AmbientDimAtCompileTime = _AmbientDim,
		Options = _Options
	};
	typedef _Scalar Scalar;
	typedef typename NumTraits<Scalar>::Real RealScalar;
	typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
	typedef Matrix<Scalar, AmbientDimAtCompileTime, 1> VectorType;
	typedef Matrix<Scalar,
				   Index(AmbientDimAtCompileTime) == Dynamic ? Dynamic : Index(AmbientDimAtCompileTime) + 1,
				   1,
				   Options>
		Coefficients;
	typedef Block<Coefficients, AmbientDimAtCompileTime, 1> NormalReturnType;
	typedef const Block<const Coefficients, AmbientDimAtCompileTime, 1> ConstNormalReturnType;

	/** Default constructor without initialization */
	EIGEN_DEVICE_FUNC inline Hyperplane() {}

	template<int OtherOptions>
	EIGEN_DEVICE_FUNC Hyperplane(const Hyperplane<Scalar, AmbientDimAtCompileTime, OtherOptions>& other)
		: m_coeffs(other.coeffs())
	{
	}

	/** Constructs a dynamic-size hyperplane with \a _dim the dimension
	 * of the ambient space */
	EIGEN_DEVICE_FUNC inline explicit Hyperplane(Index _dim)
		: m_coeffs(_dim + 1)
	{
	}

	/** Construct a plane from its normal \a n and a point \a e onto the plane.
	 * \warning the vector normal is assumed to be normalized.
	 */
	EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const VectorType& e)
		: m_coeffs(n.size() + 1)
	{
		normal() = n;
		offset() = -n.dot(e);
	}

	/** Constructs a plane from its normal \a n and distance to the origin \a d
	 * such that the algebraic equation of the plane is \f$ n \cdot x + d = 0 \f$.
	 * \warning the vector normal is assumed to be normalized.
	 */
	EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const Scalar& d)
		: m_coeffs(n.size() + 1)
	{
		normal() = n;
		offset() = d;
	}

	/** Constructs a hyperplane passing through the two points. If the dimension of the ambient space
	 * is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.
	 */
	EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1)
	{
		Hyperplane result(p0.size());
		result.normal() = (p1 - p0).unitOrthogonal();
		result.offset() = -p0.dot(result.normal());
		return result;
	}

	/** Constructs a hyperplane passing through the three points. The dimension of the ambient space
	 * is required to be exactly 3.
	 */
	EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2)
	{
		EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
		Hyperplane result(p0.size());
		VectorType v0(p2 - p0), v1(p1 - p0);
		result.normal() = v0.cross(v1);
		RealScalar norm = result.normal().norm();
		if (norm <= v0.norm() * v1.norm() * NumTraits<RealScalar>::epsilon()) {
			Matrix<Scalar, 2, 3> m;
			m << v0.transpose(), v1.transpose();
			JacobiSVD<Matrix<Scalar, 2, 3>> svd(m, ComputeFullV);
			result.normal() = svd.matrixV().col(2);
		} else
			result.normal() /= norm;
		result.offset() = -p0.dot(result.normal());
		return result;
	}

	/** Constructs a hyperplane passing through the parametrized line \a parametrized.
	 * If the dimension of the ambient space is greater than 2, then there isn't uniqueness,
	 * so an arbitrary choice is made.
	 */
	// FIXME to be consistent with the rest this could be implemented as a static Through function ??
	EIGEN_DEVICE_FUNC explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized)
	{
		normal() = parametrized.direction().unitOrthogonal();
		offset() = -parametrized.origin().dot(normal());
	}

	EIGEN_DEVICE_FUNC ~Hyperplane() {}

	/** \returns the dimension in which the plane holds */
	EIGEN_DEVICE_FUNC inline Index dim() const
	{
		return AmbientDimAtCompileTime == Dynamic ? m_coeffs.size() - 1 : Index(AmbientDimAtCompileTime);
	}

	/** normalizes \c *this */
	EIGEN_DEVICE_FUNC void normalize(void) { m_coeffs /= normal().norm(); }

	/** \returns the signed distance between the plane \c *this and a point \a p.
	 * \sa absDistance()
	 */
	EIGEN_DEVICE_FUNC inline Scalar signedDistance(const VectorType& p) const { return normal().dot(p) + offset(); }

	/** \returns the absolute distance between the plane \c *this and a point \a p.
	 * \sa signedDistance()
	 */
	EIGEN_DEVICE_FUNC inline Scalar absDistance(const VectorType& p) const { return numext::abs(signedDistance(p)); }

	/** \returns the projection of a point \a p onto the plane \c *this.
	 */
	EIGEN_DEVICE_FUNC inline VectorType projection(const VectorType& p) const
	{
		return p - signedDistance(p) * normal();
	}

	/** \returns a constant reference to the unit normal vector of the plane, which corresponds
	 * to the linear part of the implicit equation.
	 */
	EIGEN_DEVICE_FUNC inline ConstNormalReturnType normal() const
	{
		return ConstNormalReturnType(m_coeffs, 0, 0, dim(), 1);
	}

	/** \returns a non-constant reference to the unit normal vector of the plane, which corresponds
	 * to the linear part of the implicit equation.
	 */
	EIGEN_DEVICE_FUNC inline NormalReturnType normal() { return NormalReturnType(m_coeffs, 0, 0, dim(), 1); }

	/** \returns the distance to the origin, which is also the "constant term" of the implicit equation
	 * \warning the vector normal is assumed to be normalized.
	 */
	EIGEN_DEVICE_FUNC inline const Scalar& offset() const { return m_coeffs.coeff(dim()); }

	/** \returns a non-constant reference to the distance to the origin, which is also the constant part
	 * of the implicit equation */
	EIGEN_DEVICE_FUNC inline Scalar& offset() { return m_coeffs(dim()); }

	/** \returns a constant reference to the coefficients c_i of the plane equation:
	 * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
	 */
	EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs; }

	/** \returns a non-constant reference to the coefficients c_i of the plane equation:
	 * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
	 */
	EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs; }

	/** \returns the intersection of *this with \a other.
	 *
	 * \warning The ambient space must be a plane, i.e. have dimension 2, so that \c *this and \a other are lines.
	 *
	 * \note If \a other is approximately parallel to *this, this method will return any point on *this.
	 */
	EIGEN_DEVICE_FUNC VectorType intersection(const Hyperplane& other) const
	{
		EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
		Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);
		// since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests
		// whether the two lines are approximately parallel.
		if (internal::isMuchSmallerThan(det, Scalar(1))) { // special case where the two lines are approximately
														   // parallel. Pick any point on the first line.
			if (numext::abs(coeffs().coeff(1)) > numext::abs(coeffs().coeff(0)))
				return VectorType(coeffs().coeff(1), -coeffs().coeff(2) / coeffs().coeff(1) - coeffs().coeff(0));
			else
				return VectorType(-coeffs().coeff(2) / coeffs().coeff(0) - coeffs().coeff(1), coeffs().coeff(0));
		} else { // general case
			Scalar invdet = Scalar(1) / det;
			return VectorType(
				invdet * (coeffs().coeff(1) * other.coeffs().coeff(2) - other.coeffs().coeff(1) * coeffs().coeff(2)),
				invdet * (other.coeffs().coeff(0) * coeffs().coeff(2) - coeffs().coeff(0) * other.coeffs().coeff(2)));
		}
	}

	/** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this.
	 *
	 * \param mat the Dim x Dim transformation matrix
	 * \param traits specifies whether the matrix \a mat represents an #Isometry
	 *               or a more generic #Affine transformation. The default is #Affine.
	 */
	template<typename XprType>
	EIGEN_DEVICE_FUNC inline Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)
	{
		if (traits == Affine) {
			normal() = mat.inverse().transpose() * normal();
			m_coeffs /= normal().norm();
		} else if (traits == Isometry)
			normal() = mat * normal();
		else {
			eigen_assert(0 && "invalid traits value in Hyperplane::transform()");
		}
		return *this;
	}

	/** Applies the transformation \a t to \c *this and returns a reference to \c *this.
	 *
	 * \param t the transformation of dimension Dim
	 * \param traits specifies whether the transformation \a t represents an #Isometry
	 *               or a more generic #Affine transformation. The default is #Affine.
	 *               Other kind of transformations are not supported.
	 */
	template<int TrOptions>
	EIGEN_DEVICE_FUNC inline Hyperplane& transform(
		const Transform<Scalar, AmbientDimAtCompileTime, Affine, TrOptions>& t,
		TransformTraits traits = Affine)
	{
		transform(t.linear(), traits);
		offset() -= normal().dot(t.translation());
		return *this;
	}

	/** \returns \c *this with scalar type casted to \a NewScalarType
	 *
	 * Note that if \a NewScalarType is equal to the current scalar type of \c *this
	 * then this function smartly returns a const reference to \c *this.
	 */
	template<typename NewScalarType>
	EIGEN_DEVICE_FUNC inline
		typename internal::cast_return_type<Hyperplane,
											Hyperplane<NewScalarType, AmbientDimAtCompileTime, Options>>::type
		cast() const
	{
		return typename internal::
			cast_return_type<Hyperplane, Hyperplane<NewScalarType, AmbientDimAtCompileTime, Options>>::type(*this);
	}

	/** Copy constructor with scalar type conversion */
	template<typename OtherScalarType, int OtherOptions>
	EIGEN_DEVICE_FUNC inline explicit Hyperplane(
		const Hyperplane<OtherScalarType, AmbientDimAtCompileTime, OtherOptions>& other)
	{
		m_coeffs = other.coeffs().template cast<Scalar>();
	}

	/** \returns \c true if \c *this is approximately equal to \a other, within the precision
	 * determined by \a prec.
	 *
	 * \sa MatrixBase::isApprox() */
	template<int OtherOptions>
	EIGEN_DEVICE_FUNC bool isApprox(
		const Hyperplane<Scalar, AmbientDimAtCompileTime, OtherOptions>& other,
		const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
	{
		return m_coeffs.isApprox(other.m_coeffs, prec);
	}

  protected:
	Coefficients m_coeffs;
};

} // end namespace Eigen

#endif // EIGEN_HYPERPLANE_H
